   Chapter 2.R, Problem 26E

Chapter
Section
Textbook Problem

# 13–40 Calculate y ' . x 2 cos y + sin 2 y = x y

To determine

To calculate:

y'

Explanation

Rule:

i. Power rule:

ddxxn=nxn-1

ii. Sum rule:

ddxfx+g(x)=ddxfx+ddxgx

iii. Product rule:

uv'=vu'+uv'

iv. Constant multiple rule:

ddxcfx=c.ddxfx

v.

ddx(sinx)=cosx

vi.

ddxcosx=-sinx

Given:

x2cosy +sin2y=xy

Calculation:

Differentiate both side with respect to x

ddxx2cosy +sin2y=ddxxy

By using sum rule

ddxx2cosy +ddx(sin2y)=ddx(xy)

By using product rule and chain rule

cosy.ddxx2+x2.ddx(cosy)+ddx(sin2y)= yddxx+x.ddx(y)

By using power rule, chain rule and ddx(sinx)=cosx, ddxcosx=-sinx

cosy.(2x)+x2.(-siny).ddx(y)+cos2y.ddx(2y)= y(1)+x.ddx(y)

By using constant multiple rule

cosy

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